Edge-ordered Ramsey numbers
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420190" target="_blank" >RIV/00216208:11320/20:10420190 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=w6989YrlHe" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=w6989YrlHe</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2020.103100" target="_blank" >10.1016/j.ejc.2020.103100</a>
Alternative languages
Result language
angličtina
Original language name
Edge-ordered Ramsey numbers
Original language description
We introduce and study a variant of Ramsey numbers for edge-ordered graphs, that is, graphs with linearly ordered sets of edges. The edge-ordered Ramsey number (R) over bar (e)(G) of an edge-ordered graph is G the minimum positive integer N such that there exists an edge-ordered complete graph R-N on N vertices such that every 2-coloring of the edges of R-N contains a monochromatic copy of G as an edge-ordered subgraph of R-N. We prove that the edge-ordered Ramsey number (R) over bar (e)(G) is finite for every edge-ordered graph G and we obtain better estimates for special classes of edge-ordered graphs. In particular, we prove (R) over bar (e)(G) <= 2(O(n3 log n)) for every bipartite edge-ordered graph G on n vertices. We also introduce a natural class of edge-orderings, called lexicographic edge-orderings, for which we can prove much better upper bounds on the corresponding edge-ordered Ramsey numbers. (C) 2020 Elsevier Ltd. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ18-13685Y" target="_blank" >GJ18-13685Y: Model thoery and extremal combinatorics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Journal of Combinatorics
ISSN
0195-6698
e-ISSN
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Volume of the periodical
87
Issue of the periodical within the volume
June
Country of publishing house
GB - UNITED KINGDOM
Number of pages
11
Pages from-to
103100
UT code for WoS article
000531095600003
EID of the result in the Scopus database
2-s2.0-85082483173